Now showing items 33-52 of 58

    • On a conjecture of harris 

      Dan, A. (2019)
      For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ...
    • On intersection cohomology with torus actions of complexity one 

      Agustín, M.; Langlois, K. (2017-05-20)
      The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus T, one of our result determines the intersection cohomology Betti numbers of ...
    • On Lipschitz rigidity of complex analytic sets 

      Fernandes, A.; Sampaio, J.E. (2019-02-26)
      We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ...
    • On the generalized Nash problem for smooth germs and adjacencies of curve singularities 

      Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M.; Popescu-Pampu, P. (2017-12-10)
      In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space ...
    • On the geometry of strongly flat semigroups and their generalizations 

      László, T.; Némethi, A.Autoridad BCAM (2018-09-18)
      Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...
    • On the length of perverse sheaves on hyperplane arrangements 

      Budur, N.Autoridad BCAM; Liu, Y. (2019)
      Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...
    • On Zariski’s multiplicity problem at infinity 

      Sampaio, J.E. (2018-08-14)
      We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, ...
    • Perverse sheaves on semi-abelian varieties -- a survey of properties and applications 

      Liu, Y.; Maxim, L.; Wang, B. (2019-05)
      We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms ...
    • A proof of the differentiable invariance of the multiplicity using spherical blowing-up 

      Sampaio, J.E. (2018-04-21)
      In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau-Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ...
    • A proof of the integral identity conjecture, II 

      Thuong, L.Q. (2017-10-31)
      In this note, using Cluckers-Loeser’s theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.
    • Reflection maps 

      Peñafort, G. (2020)
      Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ...
    • Representation of surface homeomorphisms by tête-à-tête graphs 

      Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M.; Portilla Cuadrado, P. (2017-06-21)
      We use tête-à-tête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with non-empty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...
    • Right unimodal and bimodal singularities in positive characteristic 

      Nguyen, H.D. (2017-08-07)
      The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ...
    • Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities 

      Sampaio, J.E. (2018-06-30)
      In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ...
    • A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration 

      Thuong, L.Q. (2017-04-04)
      In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...
    • A Short Survey on the Integral Identity Conjectureand Theories of Motivic Integration 

      Thuong, L.Q. (2016-12-16)
      In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...
    • Singularities in Geometry and Topology 

      Romano, A. (2018-06-18)
      This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ...
    • Singularities of the Hilbert scheme of effective divisors 

      Dan, A. (2017-01-10)
      In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic not extensively studied. We prove that there exists such effective divisors $D$ satisfying the property: ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio, J.E. (2018-08-19)
      In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio, J.E. (2019-05-28)
      In this paper we present some applications of A'Campo-Lê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ...